Final Project Update 01

Today I felt inspired to look up alternative methods for chaos. I found some interesting explanations in "The Computational Beauty of Nature", but also some accessible material in the following links:

(Actual) Chaos Function Research

Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineers by Francis Moon

http://computing.dcu.ie/~humphrys/Notes/Neural/chaos.html

http://en.m.wikipedia.org/wiki/Logistic_map

I will experiment with these in the coming days, they seem promising

update:

The logistic map looks incredibly promising, as it also has a period from 0.0 to 1.0.
The only reason I used sine in the first place was because I wanted a function with that period. I had heard sine was used in some random functions, so I thought maybe I could make a random chaotic function from it.

The first link I posted with also the sine chaos also happened to link the logistic map article that I found independently.

Excerpts from above links

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Two chaotic regions

sin ( (1/x) (1/(1-x)) )

sin ( (1/(x/100)) (1/(1-x)) )

One chaotic region, but not so simple period

(2*sin(3/x))+(3*cos(5/x))+(4*sin(6/x))+(1*cos(3/x)

Two chaotic regions, no simple period

sin(3/x)*sin(5/(1-x))

Maximise this function: Find x that gives maximum point on y axis.

Two chaotic regions, no simple period

sin(1/x) + ( 2 * sin(1/(1-x)) )

Maximise this function: Find x that gives maximum point on y axis.